Altemate Mods

I just bought an '88 Turbo II RX7 a few weeks ago and have been having a hard time getting it to run right. Its symptoms are kind of numerous. The car runs somewhat all right until I get a little over 3k. At that point it backfires continuously. In second and third gear I can sometimes work through this and then at 4.5k the car takes off and runs pretty well as long as I rev it to 6k and don't let it fall below 4k. It has a hard time starting once it is warmed up but starts up much better cold. Also I am getting very little turbo pressure but it creeps up once in a while. Also it doesn't idle once warm... just dies every time I stop, but when its cold I can set it so that the idle jumps between 500 and 1k. Whenever I take off in 1st I have to rev it to at least 3k... sometimes 6k to keep it from dying and do a little dance on the clutch.
I have worked on it a few days now. There were a few shot vacuum lines which I replaced. I have fixed some wiring problems and put new spark plugs in. I put new oil and an oil filter in. I set the timing right and adjusted the TPS sensor to be perfect. I lost the split air pipe on the drive home, but I don't think that is an issue.
I wouldn't be posting except that the problem is just so strange. Its like there is a band around 3k to 4k where the car just runs extreemly rich, and once it gets past that band it just takes off. Any suggestions on what to do next are very appreciated.